Thursday, November 29, 2012

The math on what?

Why? Your brain events are imagining that the intelligent use of symbolism has meaning for some reason today? In any event, the history of math:

Although Gödel constructed this statement directly, the existence of at least one such statement follows from the diagonal lemma, which says that for any sufficiently strong formal system and any statement form F there is a statement p such that the system proves
p ↔ F(G(p)).

By letting F be the negation of Bew(x), we obtain the theorem
p ↔ ~Bew(G(p))
Now assume that the formal system is ω-consistent. Let p be the statement obtained in the previous section.
If p were provable, then Bew(G(p)) would be provable, as argued above. But p asserts the negation of Bew(G(p)). Thus the system would be inconsistent, proving both a statement and its negation. This contradiction shows that p cannot be provable.
If the negation of p were provable, then Bew(G(p)) would be provable (because p was constructed to be equivalent to the negation of Bew(G(p))). However, for each specific number x, x cannot be the Gödel number of the proof of p, because p is not provable (from the previous paragraph).

Thus on one hand the system supports construction of a number with a certain property (that it is the Gödel number of the proof of p), but on the other hand, for every specific number x, it can be proved that the number does not have this property. This is impossible in an ω-consistent system. Thus the negation of p is not provable.
Thus the statement p is undecidable: it can neither be proved nor disproved within the chosen system. So the chosen system is either inconsistent or incomplete. This logic can be applied to any formal system meeting the criteria. The conclusion is that all formal systems meeting the criteria are either inconsistent or incomplete. --Wikipedia

Or you could look at it symbolically given that you're living in a symbolic structure of time or a seven solar/sunday work week to this very day. Six is incomplete but the seventh day is complete, symbolically in the minds of most to this day. (It's all always symbolic, except when it isn't and you literally have to get to work. Imagine that!) You can even make it into a symbolic trinity in 666 to have a whole trinity of incompleteness etc. In other words it has been known for some time that the number of man is incomplete, however one wants to state it.

On a side note, it's interesting how the whole six thousand years number typical to the "flat earth" $tate of mind typical to progressives is often associated with the "deniers" of global warming. I.e. young earth creationists are supposedly to be associated with "six" million Holocaust deniers. Ironic? What a twisted web is woven but apparently that's some nice symbolic propaganda for "flat earth" liberals due to their ignorance, as usual. Anyway, keeping in mind that false prophets are supposedly using mathematics to model and make profitable projections about the entire globe here is an even simpler way of looking at limitations to knowledge:

Hilbert’s Programme was doomed in that it was unrealizable. In a piece of mathematics that stands as an intellectual tour-de-force of the first magnitude, Gödel demonstrated that the arithmetic with which we are all familiar is incomplete:
…that is, in any system that has a finite set of axioms and rules of inference and which is large enough to contain ordinary arithmetic, there are always true statements of the system that cannot be proved on the basis of that set of axioms and those rules of inference. This result is known as Gödel’s First Incompleteness Theorem.
Now Hilbert’s Programme also aimed to prove the essential consistency of his formulation of mathematics as a formal system. Gödel, in his Second Incompleteness Theorem, shattered that hope as well. He proved that one of the statements that cannot be proved in a sufficiently strong formal system is the consistency of the system itself. In other words, if arithmetic is consistent then that fact is one of the things that cannot be proved in the system. It is something that we can only believe on the basis of the evidence, or by appeal to higher axioms. This has been succinctly summarized by saying that if a religion is something whose foundations are based on faith, then mathematics is the only religion that can prove it is a religion!
(God’s Undertaker: Has Science Buried God?
by John Lennox :52)

Projections vary, but follow the mathematics of money or symbols of debt to their end and you may find the root of all evil.